diff options
| -rw-r--r-- | doc/fold.md | 43 | ||||
| -rw-r--r-- | docs/doc/fold.html | 36 |
2 files changed, 79 insertions, 0 deletions
diff --git a/doc/fold.md b/doc/fold.md index a5097ed0..6300e715 100644 --- a/doc/fold.md +++ b/doc/fold.md @@ -2,6 +2,49 @@ # Fold and Insert +<!--GEN +f ← •BQN fn ← "-" ⋄ ft ← Highlight fn +xt ← Highlight∘•Repr¨ xv ← 2‿0‿5‿3‿4‿2 +zt ← Highlight∘•Repr¨ F˜`⌾⌽ xv +d ← 56‿40 + +rc ← At "class=code|stroke-width=1.5|rx=12" +Ge ← "g"⊸At⊸Enc +g ← "font-size=21px|fill=currentColor|stroke-linecap=round|text-anchor=middle|font-family=BQN,monospace" +bg ← "class=bluegreen|stroke-width=3|style=fill:none|opacity=0.7" +lg ← "class=lilac|stroke-width=2" + +Text ← ("text" Attr "dy"‿"0.32em"∾ ·Pos d⊸×)⊸Enc +Path ← "path" Elt "d"≍○<⊢ +Line ← "line" Elt (⍉"xy"≍⌜"12")≍˘○⥊ ·FmtNum ·d⊸ע⊢ + +Brak ← { + l ← 6‿15 + P ← ∾"M l l "∾¨ ·FmtNum∘⥊ ∾ + Path ∾ (((-⊸≍0.4)+0‿¯1⊏𝕨)((0‿¯1×l)+d×≍)⌜𝕩) P¨ ≍○<⟜⌽ -⌾⊑⊸≍l +} + +_pair ← {1(↓𝔽-⊸↓)⊢} +tx ← ↕≠xt ⋄ ty ← 0.8+5×↕2 +sy ← (2÷˜+´ty)-3×0.5-˜(↕÷-⟜1) ≠sx←2÷˜+_pair tx +tp ← tx≍¨⊑ty ⋄ sp ← sx≍¨sy +dim ← ⟨2.5+≠tx,0.8+1⊑ty⟩ ⋄ sh ← ¯2.3‿0 +lp ← 0.35 + +((∾˜d)×((-∾+˜)1‿0.3)+sh∾dim) SVG g Ge ⟨ + "rect" Elt rc ∾ (Pos d×sh)∾"width"‿"height"≍˘FmtNum d×dim + lg Ge Line¨ ∾⟨ + tp (≍+·≍⟜-·(⊢×lp÷1⊸⊑)-)¨ ¯0.25‿0<⊸(+ ∾ ⊣-˜¯1⊏⊢)sp + ((lpׯ0.5‿1≍1.2‿¯0.5)+≍)¨_pair sp + ⟨sx {⍉(≍˜𝕨)≍(≍⟜-lp)+𝕩≍1⊑ty}○⊑ sy⟩ + ⟩ + "text-anchor=end" Ge (¯1.1≍¨ty) Text¨ ≍○<⟜(ft∾(Highlight"´")∾⊢) "𝕩" + (tp∾<(⊑sx)≍1⊑ty) Text¨ xt∾⊏zt + sp Text¨ (¯1↓xt) ∾⟜ft⊸∾¨ 1↓zt + bg Ge tx Brak ⊑ty +⟩ +--> + The closely related 1-modifiers Fold (`´`) and Insert (`˝`) apply a dyadic operand function `𝔽` repeatedly between elements or major cells of `𝕩`. Neither is quite like the APL2-style Reduce operator (`/` or `⌿` in APL), although I sometimes use the term "reduction" to mean either Fold or Insert. There are a bunch of other names like "accumulate" and "aggregate" for this class of calculations—I don't know which is best but I know "catamorphism" is worst. A distinguishing feature of APL-family reductions is that they don't use an initial value, and try to derive an "identity element" from the operand if the argument array is empty. BQN retains this capability but also allows the programmer to supply an initial value as `𝕨`. diff --git a/docs/doc/fold.html b/docs/doc/fold.html index 2ea1ceeb..5ae46961 100644 --- a/docs/doc/fold.html +++ b/docs/doc/fold.html @@ -5,6 +5,42 @@ </head> <div class="nav"><a href="https://github.com/mlochbaum/BQN">BQN</a> / <a href="../index.html">main</a> / <a href="index.html">doc</a></div> <h1 id="fold-and-insert">Fold and Insert</h1> +<svg viewBox='-184.8 -12 588 288'> + <g font-size='21px' fill='currentColor' stroke-linecap='round' text-anchor='middle' font-family='BQN,monospace'> + <rect class='code' stroke-width='1.5' rx='12' x='-128.8' y='0' width='476' height='264'/> + <g class='lilac' stroke-width='2'> + <line x1='1.225' y1='46' x2='12.775' y2='178'/> + <line x1='57.508' y1='46' x2='68.492' y2='148'/> + <line x1='113.96' y1='46' x2='124.04' y2='118'/> + <line x1='170.8' y1='46' x2='179.2' y2='88'/> + <line x1='228.9' y1='46' x2='233.1' y2='58'/> + <line x1='275.1' y1='46' x2='270.9' y2='58'/> + <line x1='74.2' y1='176' x2='51.52' y2='185'/> + <line x1='130.2' y1='146' x2='107.52' y2='155'/> + <line x1='186.2' y1='116' x2='163.52' y2='125'/> + <line x1='242.2' y1='86' x2='219.52' y2='95'/> + <line x1='28' y1='206' x2='28' y2='218'/> + </g> + <g text-anchor='end'> + <text dy='0.32em' x='-61.6' y='32'>𝕩</text> + <text dy='0.32em' x='-61.6' y='232'><tspan class='Function'>-</tspan><tspan class='Modifier'>´</tspan>𝕩</text> + </g> + <text dy='0.32em' x='0' y='32'><tspan class='Number'>2</tspan></text> + <text dy='0.32em' x='56' y='32'><tspan class='Number'>0</tspan></text> + <text dy='0.32em' x='112' y='32'><tspan class='Number'>5</tspan></text> + <text dy='0.32em' x='168' y='32'><tspan class='Number'>3</tspan></text> + <text dy='0.32em' x='224' y='32'><tspan class='Number'>4</tspan></text> + <text dy='0.32em' x='280' y='32'><tspan class='Number'>2</tspan></text> + <text dy='0.32em' x='28' y='232'><tspan class='Number'>6</tspan></text> + <text dy='0.32em' x='28' y='192'><tspan class='Number'>2</tspan><tspan class='Function'>-</tspan><tspan class='Number'>¯4</tspan></text> + <text dy='0.32em' x='84' y='162'><tspan class='Number'>0</tspan><tspan class='Function'>-</tspan><tspan class='Number'>4</tspan></text> + <text dy='0.32em' x='140' y='132'><tspan class='Number'>5</tspan><tspan class='Function'>-</tspan><tspan class='Number'>1</tspan></text> + <text dy='0.32em' x='196' y='102'><tspan class='Number'>3</tspan><tspan class='Function'>-</tspan><tspan class='Number'>2</tspan></text> + <text dy='0.32em' x='252' y='72'><tspan class='Number'>4</tspan><tspan class='Function'>-</tspan><tspan class='Number'>2</tspan></text> + <g class='bluegreen' stroke-width='3' style='fill:none' opacity='0.7'><path d='M-22.4 17l-6 15l6 15M302.4 17l6 15l-6 15'/></g> + </g> +</svg> + <p>The closely related 1-modifiers Fold (<code><span class='Modifier'>´</span></code>) and Insert (<code><span class='Modifier'>˝</span></code>) apply a dyadic operand function <code><span class='Function'>𝔽</span></code> repeatedly between elements or major cells of <code><span class='Value'>𝕩</span></code>. Neither is quite like the APL2-style Reduce operator (<code><span class='Function'>/</span></code> or <code><span class='Value'>⌿</span></code> in APL), although I sometimes use the term "reduction" to mean either Fold or Insert. There are a bunch of other names like "accumulate" and "aggregate" for this class of calculations—I don't know which is best but I know "catamorphism" is worst.</p> <p>A distinguishing feature of APL-family reductions is that they don't use an initial value, and try to derive an "identity element" from the operand if the argument array is empty. BQN retains this capability but also allows the programmer to supply an initial value as <code><span class='Value'>𝕨</span></code>.</p> <h2 id="fold">Fold</h2> |